Extended F-expansion Method and Its Application to the Variable-coefficient Fractional Nonlinear Schro¨dinger Equation

Hao Libin, Zhao Xiaoshan
Proceedings of 2024 International Conference on Machine Learning and Intelligent Computing, PMLR 245:297-307, 2024.

Abstract

In this paper, under the definition of conformable fractional derivatives, we use the extended Fexpansion method and obtain the exact solution of the variable-coefficient factional nonlinear Schrodinger equation (FNLSE), including rational function solutions and Jacobi elliptic function solution. When the mode m of these solutions tends to 1 and 0, the hyperbolic function solution, triangular function solution, and light and dark solitary wave solution are obtained. The correlation diagram of the exact solution is plotted, and the effect of different parameters on the solution structure is deeply analyzed. By selecting a large number of parameters and comparing the graphical analysis of different solutions obtained using this method, we have identified properties related to the nonlinear Schro¨dinger equation with variable coefficients and summarized relevant theorems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v245-libin24a, title = {Extended F-expansion Method and Its Application to the Variable-coefficient Fractional Nonlinear Schro¨dinger Equation}, author = {Libin, Hao and Xiaoshan, Zhao}, booktitle = {Proceedings of 2024 International Conference on Machine Learning and Intelligent Computing}, pages = {297--307}, year = {2024}, editor = {Nianyin, Zeng and Pachori, Ram Bilas}, volume = {245}, series = {Proceedings of Machine Learning Research}, month = {26--28 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v245/main/assets/libin24a/libin24a.pdf}, url = {https://proceedings.mlr.press/v245/libin24a.html}, abstract = {In this paper, under the definition of conformable fractional derivatives, we use the extended Fexpansion method and obtain the exact solution of the variable-coefficient factional nonlinear Schrodinger equation (FNLSE), including rational function solutions and Jacobi elliptic function solution. When the mode m of these solutions tends to 1 and 0, the hyperbolic function solution, triangular function solution, and light and dark solitary wave solution are obtained. The correlation diagram of the exact solution is plotted, and the effect of different parameters on the solution structure is deeply analyzed. By selecting a large number of parameters and comparing the graphical analysis of different solutions obtained using this method, we have identified properties related to the nonlinear Schro¨dinger equation with variable coefficients and summarized relevant theorems.} }
Endnote
%0 Conference Paper %T Extended F-expansion Method and Its Application to the Variable-coefficient Fractional Nonlinear Schro¨dinger Equation %A Hao Libin %A Zhao Xiaoshan %B Proceedings of 2024 International Conference on Machine Learning and Intelligent Computing %C Proceedings of Machine Learning Research %D 2024 %E Zeng Nianyin %E Ram Bilas Pachori %F pmlr-v245-libin24a %I PMLR %P 297--307 %U https://proceedings.mlr.press/v245/libin24a.html %V 245 %X In this paper, under the definition of conformable fractional derivatives, we use the extended Fexpansion method and obtain the exact solution of the variable-coefficient factional nonlinear Schrodinger equation (FNLSE), including rational function solutions and Jacobi elliptic function solution. When the mode m of these solutions tends to 1 and 0, the hyperbolic function solution, triangular function solution, and light and dark solitary wave solution are obtained. The correlation diagram of the exact solution is plotted, and the effect of different parameters on the solution structure is deeply analyzed. By selecting a large number of parameters and comparing the graphical analysis of different solutions obtained using this method, we have identified properties related to the nonlinear Schro¨dinger equation with variable coefficients and summarized relevant theorems.
APA
Libin, H. & Xiaoshan, Z.. (2024). Extended F-expansion Method and Its Application to the Variable-coefficient Fractional Nonlinear Schro¨dinger Equation. Proceedings of 2024 International Conference on Machine Learning and Intelligent Computing, in Proceedings of Machine Learning Research 245:297-307 Available from https://proceedings.mlr.press/v245/libin24a.html.

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